I bought an entry-level DSLR at Christmas time (Nikon D3000 with 18-55mm and 55-200mm lenses) and have been figuring my way around the camera. I know the very basics, but want to take a class and can't logistically take one offered in my area. Are there good online classes for learning about lighting, exposure, composition, etc.? Or maybe sites with good exercises for beginners?

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise.
If this question can be reworded to fit the rules in the help center, please edit the question.

They are not specifically all photography related, more like art/creativity stuff. But their photography classes are superb - so superb to the point I was willing to pay for them. Some are free, but to get the archive, download, etc, you will need to pay for some. But they are worth it!

Oh dear, this is going to be a hard one to answer. Since there's so much courseware. But I'll share the ones I have appreciated. Unfortunately not a lot of this stuff mentioned below will get you college credits (if any), but you'd probably be pretty pleased with yourself at the end of it all being in the situation of knowing rather than not knowing. I wouldn't be surprised if you end up coming back to these to supplement for-credit courseware.

General:

It goes without saying that hopefully Q and A sites such as photo.stackexchange.com (or whatever its final name will be) will someday be the source of course reading material.

Photo.net is another huge source of articles. Some mercifully abridged, glossing over everything, for the most innocent of new photography learners--others surprisingly deep. If you haven't read them all, you should. They make a great course just as they are. I still go back there and discover that something well understood and worth heeding goes completely unheeded by me for far too long. Alumnis of photo.net education should return often. Photo.net exist partly thanks to people like Philip Greenspun and his photography buddies. Photo.net and slightly gated online discussion groups and bulletin boards tend to be generalist, but there are some focusing on one system at a time (the Nikon system for instance). Or specialization (children photography for instance). They are wonderful. In fact, never read a Photo.net article without also reading in the comments of the readers chiming in. It's never a waste of time in my book. What people discuss can be surprisingly deep, so the few dollars required annually to register for a discussion forum related to your photography craft is money well spent. Definitely be a team player here: learn and share likewise.

Total Training and Lynda.com:

Incredible resources at a subscription price you can't ignore. All laid out clearly for the new comer or the photographers who knows that they'll need to be power users from day one. Post processing with Adobe Photoshop, presentation and media with Adobe InDesign, Adobe Illustrator, Adobe Flash and so on. They are really great for a first pass through the material, so that you know what's possible or probable with these software at your disposal. From there, it's good to couple these videos with a well bookmarked notes so that you can dig up the details without having to find the exact minute and second tick mark required to relearn something from these videos.

Post processing:

Luminous Landscape by Michael Reichmann and his photography education friends all did a great job distilling everything you might want to know down to short videos between the time the RAW files leaves your camera and ends up hanging on the wall. I would still read 2000 pages on color management because I am insane like that, but if you want the short version--I can't think of anyone better.

For photography lighting:

David Hobby and his Strobist.com has tried to provide some fantastic free or nearly free material. He confesses to stand on the shoulders of giants, such as the late photography lighting educator Dean Collins and recommends Dean's material highly. I think both are fantastic for lighting. David and Dean's videos have a courseware component to them. They illustrate how it's done, why it's done, and challenge you to replicate the successes in your own DIY (or sourced from commercial light modifier makers) efforts. It seems to me that David might go into talk about lighting for cinema in the next little while on Strobist.com, stretching himself and forcing himself to learn just a tad more than the rest of us just a few hours ahead of us. That's big. That takes a great deal of confidence, hard-work and research so I wish him the best.

Transition to video:

Vincent Laforet, Chase Jarvis, B&H, and creativeLIVE all came together to address the thousands of issues that we haven't thought about in our transition from stills to video in a three day web-casted workshop. It's a really good basecamp to figure out how to navigate the terrains of your eventual transition to video. They blog too, and what Vincent and Chase has blogged over the year probably can't ever be fit into a three day workshop no matter how they squeeze.

Marketing:

Dan Heller has been writing about photography, the business and marketing of photography for a long while now. And has some great ideas to share. There's no set 'class'. Lots of great material that you'll want to at least read once-through and decide for yourself the merit of each point.

I think it's really really really wonderful that these people share so much of their time with us through blogs, videos, writing and workshops. They have been keen on helping to raise the art/biz/sci average for all photographers. They do it for a variety of reasons, for the fame that will keep their calendars booked with the clients they want to work with; or just so they never have to explain something for the Nth time with their friends; or even so that their children would someday know what mom and dad did.

Off the buzzword charts:

Video courseware is not a new invention, it's been around since before Betacam and VHS. So do know that folks have been making actually timeless classics for a long long while. Check your reference libraries. You'd be quite surprised by the relevance and creativity behind some of the tips being shared from some of the old old videos. On marketing, on business, on the very act of taking photos. I mean, we are still capturing light--that hasn't changed at all for many many years.

http://www.brighthub.com/multimedia/photography.aspx offers a lot of quick tipps. Many are not really in detail, but to get an overview over a topic it is nice and quick. Other topics like composition are treated in several articles and therefore provide more in depth information.

The B&H Event Space has good videos on a variety of topics. They're not very well organized, but as good as some of the paid videos I've seen from other websites (sometimes offered by the same instructor). When looking at the playlist look for videos that are 1-2 hours long as anything shorter than that is probably a product showcase video (still informative, but not the best videos in the playlist).